What generation is my ipad model isA1416 SERIAL NUMBER IS DYTHK7Z4DJ8R

can you try providing the model number instead of serial no,?

iPad (4th generation)

• Year: Late 2012
• Capacity: 16, 32, 64, 128 GB
• Model number (on the back cover):
  A1458 on the iPad (4th generation) Wi-Fi

That is an iPad 4th Generation with Wifi and Celluar on a Verizon or Sprint Network. I believe.
Here is a link to a website where I did the search: http://goo.gl/yiHmkA

Serial Number: DN6FXJPYDKPH
Model:- iPad 2 (WiFi)
Codename:- No codename assigned.
Build Country:- We don't know where this unit was built.
Build Year:- This unit was built in the first half of 2011.
Build Week- Week 26 (June)
Production Nr.:- This unit was number 2038 to be built that week.Serial Number: DN6FXJPYDKPH
Model:- iPad 2 (WiFi)
Codename:- No codename assigned.
Build Country:- We don't know where this unit was built.
Build Year:- This unit was built in the first half of 2011.
Build Week- Week 26 (June)
Production Nr.:- This unit was number 2038 to be built that week.

http://www.appleserialnumberinfo.com/Desktop/index.php

2nd gen.

Suggest reading this for best details:
http://www.techhive.com/article/2049920/how-to-tell-which-ipad-model-you-have.html
You do not need the serial number. Check the "A" number and look at above article for your answer.
Good luck!

on the backside of the iPad is a model number:

Model iPad (1st generation) iPad 2 iPad (3rd generation) iPad (4th generation) iPad Air iPad Air 2 Picture Model Number[99] A1219 (Wi-Fi)
A1337 (Wi-Fi + 3G) A1395 (Wi-Fi)
A1396 (GSM model)
A1397 (CDMA model) A1416 (Wi-Fi)
A1403 (Wi-Fi + Cellular (VZ))
A1430 (Wi-Fi + Cellular) A1458 (Wi-Fi)
A1460 (Wi-Fi + Cellular (MM))
A1459 (Wi-Fi + Cellular) A1474 (Wi-Fi)
A1475 (Wi-Fi + Cellular) A1566 (Wi-Fi)
A1567 (Wi-Fi + Cellular How to find iPad IMEI ICCID serial number
http://en.wikipedia.org/wiki/List_of_iOS_devices#iPad

it is an Ipad 4th generation (WiFi only)
Lookup Mac Specs By Serial Number Order Model EMC Number Model ID EveryMac...

iPad 4th Gen (Wi-Fi Only) 1.4 GHz* Apple A6X Intro Date: October 23, 2012* Disc Date: October 16, 2014** Order No: MD510LL/A* Model No: A1458 (EMC 2604*) Subfamily: iPad 4th Gen (Wi-Fi) Model ID: iPad3,4 Std RAM: 1 GB* Std VRAM: None Std Storage: 16, 32, 64, 128 GB* Std Optical: None Complete iPad 4th Gen (Wi-Fi Only) Specs

check the model nr. on the back side:
Apple Device Model Number
1iPad Wi-Fi (Original/1st Gen)A12191
iPad Wi-Fi/3G/GPS (Original/1st Gen)A13371
iPad 2 (Wi-Fi Only)A13951
iPad 2 (Wi-Fi/GSM/GPS)A13961
iPad 2 (Wi-Fi/CDMA/GPS)A13971
iPad 2 (Wi-Fi Only, iPad2,4)A13951
iPad 3rd Gen (Wi-Fi Only)A14161
iPad 3rd Gen (Wi-Fi/Cellular AT&T/GPS)A14301
iPad 3rd Gen (Wi-Fi/Cellular Verizon/GPS)A14031
iPad 4th Gen (Wi-Fi Only)A14581
iPad 4th Gen (Wi-Fi/AT&T/GPS)A14591i
iPad 4th Gen (Wi-Fi/Verizon & Sprint/GPS)A14601
iPad Air (Wi-Fi Only)A14741
iPad Air (Wi-Fi/Cellular)A14751